A cervical intervertebral prosthesis is known (U.S. Pat. No. 6,368,350) which is composed of an upper connection plate and a lower connection plate for connection to the adjacent vertebral bodies, and of a hinge core which, with one connection plate, forms a hinge with a convex hinge surface on the underside of the upper connection plate and with a concave hinge surface on the top side of the hinge core. The hinge core bears on the other connection plate via a slide surface which extends parallel to the direction of extension of the connection plate and which permits a relative translatory movement of the hinge core in this direction with respect to the lower connection plate. This relative movement is limited by means of the slide surface being restricted by a vertical edge. In the known prosthesis, the hinge surface of the hinge core has a very shallow dish-like configuration. This is customary, because it is possible in this way to achieve a low specific surface load. However, this entails the risk that, if the ligaments connecting the relevant vertebral bodies to one another are too weak or stretched, the prosthesis parts may come loose from one another. Although it is known (U.S. Pat. No. 5,895,428) to connect the prosthesis parts to one another by means of a screw passing centrally through the hinge surfaces, this cannot be done in conjunction with the abovementioned translatory freedom of movement of the hinge core parallel to the extension of the connection plates, and, in any case, this is impossible in a cervical prosthesis, because of the confined space.